Final answer:
The terms to fill the blanks in the given statement are 'adjacent angles.' These angles are co-planar, share a common vertex and side, and do not overlap. Understanding relations between angles and vectors such as orthogonal and parallel vectors is also beneficial in geometry.
Step-by-step explanation:
The blank spaces in the statement '……………… are two co-planar, no overlapping angles that share a common vertex and a common side.' are meant to be filled with the term adjacent angles. Adjacent angles are two angles that meet these specific conditions: they are in the same plane (co-planar), they do not overlap, they have a common vertex (the point where they meet), and they share one common side.
An important concept related to vectors and angles is the idea of orthogonal vectors, which are two vectors with directions that differ by exactly 90°, making them perpendicular to each other. Conversely, parallel vectors are two vectors that share the exact same direction. Understanding these relationships helps in the interpretation of geometric constructions like the parallelogram rule for vector addition and with coordinate systems such as the polar coordinate system.